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

Author

T. D. Noe, Jul 28 2006

Keywords

• fini
• nonn

Comments

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

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)

Programs

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]]