Euler 169 - Diatonic sequence.ipynb

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    "Euler Problem 169\n",
    "=================\n",
    "\n",
    "Define f(0)=1 and f(n) to be the number of different ways n can be expressed as a sum of integer powers of 2 using each power no more than twice.\n",
    "\n",
    "For example, f(10)=5 since there are five different ways to express 10:\n",
    "\n",
    "    1 + 1 + 8\n",
    "    1 + 1 + 4 + 4\n",
    "    1 + 1 + 2 + 2 + 4\n",
    "    2 + 4 + 4\n",
    "    2 + 8\n",
    "\n",
    "What is f(10<sup>25</sup>)?\n"
   ]
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      "178653872807\n"
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    "F = {}\n",
    "F[0] = F[1] = 1\n",
    "def f(n):\n",
    "    if n in F:\n",
    "        return F[n]\n",
    "    if (n % 2):\n",
    "        val = f(n//2)\n",
    "    else:\n",
    "        val = f(n//2) + f(n//2-1)\n",
    "    F[n] = val\n",
    "    return val\n",
    "\n",
    "print(f(10**25))"
   ]
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