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A272267 The union of centered square numbers (A001844) and centered 9-gonal numbers (A060544). 2


%S 1,5,10,13,25,28,41,55,61,85,91,113,136,145,181,190,221,253,265,313,

%T 325,365,406,421,481,496,545,595,613,685,703,761,820,841,925,946,1013,

%U 1081,1105,1201,1225,1301,1378,1405,1513,1540,1625,1711,1741,1861,1891

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

%H Colin Barker, <a href="/A272267/b272267.txt">Table of n, a(n) for n = 1..1000</a>

%F Conjectures:

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

%F 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).

%o (PARI)

%o cpg(m, n) = m*n*(n-1)/2+1 \\ n-th centered m-gonal number

%o cpgr(m, r) = n=1; L=List(); while((t=cpg(m, n))<r, listput(L, t); n++); Vec(L)

%o cpgcpgs(p, q, r) = setunion(cpgr(p, r), cpgr(q, r))

%o cpgcpgs(4, 9, 2000)

%Y Cf. A001844, A060544, A272266.

%K nonn

%O 1,2

%A _Colin Barker_, Apr 24 2016

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Last modified October 17 00:03 EDT 2019. Contains 328103 sequences. (Running on oeis4.)