A342250 Number of ways to write n as an ordered sum of seven powers of 2.

1, 7, 21, 42, 77, 126, 168, 218, 294, 357, 427, 546, 637, 672, 756, 840, 854, 966, 1134, 1218, 1302, 1408, 1484, 1554, 1680, 1827, 1995, 2002, 1925, 2016, 1988, 1904, 2142, 2352, 2282, 2352, 2534, 2520, 2604, 2954, 3080, 3276, 3262, 3234, 3150, 3248, 3164, 3402, 3640

Offset: 7

Author

Ilya Gutkovskiy, Mar 07 2021

Keywords

• nonn
• look

Links

• Robert Israel, Table of n, a(n) for n = 7..10000

Crossrefs

Cf. A000079, A023359, A073267, A151759, A151760, A151761, A151762, A209229, A342247, A342251, A342252, A342254.

Programs

Maple

N:= 100:
S:= add(x^(2^j),j=0..ilog2(N-6))^7:
[seq](coeff(S,x,j),j=7..N); # Robert Israel, Feb 26 2023

Mathematica

nmax = 55; CoefficientList[Series[Sum[x^(2^k), {k, 0, Floor[Log[2, nmax]] + 1}]^7, {x, 0, nmax}], x] // Drop[#, 7] &

Formula

G.f.: ( Sum_{k>=0} x^(2^k) )^7.