A369734 Number of solutions to 1^2*k_1 + 2^2*k_2 + ... + n^2*k_n = 1, where k_i are from {-1,0,1}, i=1..n.

0, 1, 1, 1, 1, 3, 8, 17, 35, 79, 177, 409, 995, 2475, 6336, 16078, 41401, 107304, 279550, 736032, 1950000, 5199850, 13950852, 37576658, 101670863, 276228026, 753114256, 2060995699, 5658663542, 15583477334, 43039552072, 119179072495, 330836308272, 920537185436

Offset

0,6

Links

Table of n, a(n) for n=0..33.

Formula

a(n) = [x^1] Product_{k=1..n} (x^(k^2) + 1 + 1/x^(k^2)).

Mathematica

Table[Coefficient[Product[(x^(k^2) + 1 + 1/x^(k^2)), {k, 1, n}], x, 1], {n, 0, 32}]

Crossrefs

Cf. A007576, A063866, A350249, A369433, A369628, A369735.

Sequence in context: A159217 A052996 A112523 * A147419 A106691 A140176

Adjacent sequences: A369731 A369732 A369733 * A369735 A369736 A369737

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 30 2024

Status

approved