A238313 Alternating square row sums of the table A072233 (A008284).

1, 1, 0, 1, 3, 1, 3, 3, 10, 18, 12, 26, 39, 57, 59, 116, 201, 219, 325, 416, 625, 810, 1074, 1447, 2345, 3078, 3530, 5084, 6790, 9063, 11674, 15580, 20887, 27537, 33640, 45065, 61297, 76883, 96889, 126243, 169268, 210005, 262068, 337445, 438197, 552346, 686794, 865904, 1128611, 1407533, 1732572

Offset

0,5

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..90

Formula

a(n) = sum((-1)^(n-k)*p(n,k)^2,k=0..n), where p(n,k) is the number of partitions of n into k positive parts (A072233, A008284).

Mathematica

pnkList[n_] := Table[Length[IntegerPartitions[n, {k}]], {k, 0, n}]
Table[Total[Table[(-1)^(n-k), {k, 0, n}] Map[#^2 &, pnkList[n]]], {n, 0, 50}]

Crossrefs

Cf. A072233, A008284.

Sequence in context: A238784 A336765 A147610 * A163270 A098743 A283484

Adjacent sequences: A238310 A238311 A238312 * A238314 A238315 A238316

Keyword

nonn

Author

Emanuele Munarini, Feb 24 2014

Status

approved