A272267 The union of centered square numbers (A001844) and centered 9-gonal numbers (A060544).

1, 5, 10, 13, 25, 28, 41, 55, 61, 85, 91, 113, 136, 145, 181, 190, 221, 253, 265, 313, 325, 365, 406, 421, 481, 496, 545, 595, 613, 685, 703, 761, 820, 841, 925, 946, 1013, 1081, 1105, 1201, 1225, 1301, 1378, 1405, 1513, 1540, 1625, 1711, 1741, 1861, 1891

Offset

1,2

Links

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

Formula

Conjectures:

a(n) = a(n-1)+2*a(n-5)-2*a(n-6)-a(n-10)+a(n-11) for n>11.

G.f.: x*(1+4*x+5*x^2+3*x^3+12*x^4+x^5+5*x^6+4*x^7+x^10) / ((1-x)^3*(1+x+x^2+x^3+x^4)^2).

Prog

(PARI)
cpg(m, n) = m*n*(n-1)/2+1 \\ n-th centered m-gonal number
cpgr(m, r) = n=1; L=List(); while((t=cpg(m, n))<r, listput(L, t); n++); Vec(L)
cpgcpgs(p, q, r) = setunion(cpgr(p, r), cpgr(q, r))
cpgcpgs(4, 9, 2000)

Crossrefs

Cf. A001844, A060544, A272266.

Sequence in context: A313450 A292268 A309593 * A195735 A061145 A345261

Adjacent sequences: A272264 A272265 A272266 * A272268 A272269 A272270

Keyword

nonn

Author

Colin Barker, Apr 24 2016

Status

approved