A121405 Numbers that are not the sum of distinct pentagonal numbers (A000326).

2, 3, 4, 7, 8, 9, 10, 11, 14, 15, 16, 19, 20, 21, 24, 25, 26, 29, 30, 31, 32, 33, 37, 38, 42, 43, 44, 45, 46, 49, 50, 54, 55, 59, 60, 61, 65, 66, 67, 72, 77, 80, 81, 84, 89, 94, 95, 96, 100, 101, 102, 107, 112, 116, 124, 136, 137, 141, 142, 147, 159

Offset

1,1

Comments

For sums of distinct generalized pentagonal numbers (A001318), only 4 and 11 are not representable.

Links

Table of n, a(n) for n=1..61.

Mathematica

nn=50; a=Table[n(3n-1)/2, {n, nn}]; t=Rest[CoefficientList[Series[Product[(1+x^a[[k]]), {k, nn}], {x, 0, a[[ -1]]}], x]]; Flatten[Position[t, 0]]

Crossrefs

Cf. A025524 (number of numbers not the sum of distinct n-th-order polygonal numbers)

Cf. A007419 (largest number not the sum of distinct n-th-order polygonal numbers)

Cf. A053614, A001422 (corresponding sequences for triangular and square numbers)

Sequence in context: A037466 A285405 A305441 * A330217 A231003 A171551

Adjacent sequences: A121402 A121403 A121404 * A121406 A121407 A121408

Keyword

fini,nonn

Author

T. D. Noe, Jul 28 2006

Status

approved