A272266 The union of squares (A000290) and 10-gonal numbers (A001107).

1, 4, 9, 10, 16, 25, 27, 36, 49, 52, 64, 81, 85, 100, 121, 126, 144, 169, 175, 196, 225, 232, 256, 289, 297, 324, 361, 370, 400, 441, 451, 484, 529, 540, 576, 625, 637, 676, 729, 742, 784, 841, 855, 900, 961, 976, 1024, 1089, 1105, 1156, 1225, 1242, 1296

Offset: 1

Author

Colin Barker, Apr 24 2016

Keywords

• nonn

Links

• Colin Barker, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000290, A001107, A272267.

Programs

PARI

pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ The n-th m-gonal number
pgr(m, r) = n=1; L=List(); while((t=pg(m, n))
				

Formula

Conjectures:

a(n) = a(n-1)+2*a(n-3)-2*a(n-4)-a(n-6)+a(n-7) for n>7.

G.f. x*(1+3*x+5*x^2-x^3-x^5+x^6) / ((1-x)^3*(1+x+x^2)^2).