A129504 Row sums of triangle A129503.
1, 2, 3, 5, 8, 12, 17, 24, 34, 48, 67, 92, 124, 164, 213, 273, 347, 439, 554, 698, 878, 1102, 1379, 1719, 2133, 2633, 3232, 3944, 4784, 5768, 6913, 8238, 9765, 11520, 13534, 15844, 18494, 21536, 25031, 29050, 33675, 39000, 45132, 52192, 60316, 69656, 80381
Offset: 1
Keywords
Examples
a(7) = 17 = sum of row 7 terms of A129503: (1 + 6 + 0 + 10 + 0 + 0 + 0).
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..1000
Programs
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PARI
a(n)=sum(k=0, logint(n, 2), binomial(n-2^k+k, k)) \\ Andrew Howroyd, Aug 09 2018
Formula
a(n) = Sum_{k >= 0, 2^k <= n} binomial(n - 2^k + k, k). - Andrew Howroyd, Aug 09 2018
Extensions
Offset and a(9) corrected and a(11)-a(47) from Andrew Howroyd, Aug 09 2018