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
Keywords
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
Programs
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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))
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).