cp's OEIS Frontend

A141534 Derived from the centered polygonal numbers: start with the first triangular number, then the sum of the first square number and the second triangular number, then the sum of first pentagonal number, the second square number and the third triangular number, and so on and so on...

%I A141534 #22 Jun 17 2017 03:06:08
%S A141534 1,4,11,26,55,105,184,301,466,690,985,1364,1841,2431,3150,4015,5044,
%T A141534 6256,7671,9310,11195,13349,15796,18561,21670,25150,29029,33336,38101,
%U A141534 43355,49130,55459,62376,69916,78115,87010,96639,107041,118256,130325
%N A141534 Derived from the centered polygonal numbers: start with the first triangular number, then the sum of the first square number and the second triangular number, then the sum of first pentagonal number, the second square number and the third triangular number, and so on and so on...
%C A141534 Consider the array of triangular, square and centered polygonal numbers (irregular variant of A086272 and A086273):
%C A141534 1   3   6  10  15  21  28  36  45  55  A000217
%C A141534 1   4   9  16  25  36  49  64  81 100  A000290
%C A141534 1   6  16  31  51  76 106 141 181 226  A005891
%C A141534 1   7  19  37  61  91 127 169 217 271  A003215
%C A141534 1   8  22  43  71 106 148 197 253 316  A069099
%C A141534 1   9  25  49  81 121 169 225 289 361  A016754
%C A141534 1  10  28  55  91 136 190 253 325 406  A060544
%C A141534 1  11  31  61 101 151 211 281 361 451  A062786
%C A141534 1  12  34  67 111 166 232 309 397 496  A069125
%C A141534 1  13  37  73 121 181 253 337 433 541  A003154
%C A141534 1  14  40  79 131 196 274 365 469 586  A069126
%C A141534 1  15  43  85 141 211 295 393 505 631  A069127
%C A141534 etc. The sequence contains the antidiagonal sums of this array. - _R. J. Mathar_, Jun 05 2011
%C A141534 For comparison, the antidiagonal sums of A086270 are essentially A006522 starting at the 4th term. - _R. J. Mathar_, Sep 20 2008
%H A141534 Vincenzo Librandi, <a href="/A141534/b141534.txt">Table of n, a(n) for n = 1..10000</a>
%H A141534 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A141534 a(n) = (n-1)*(n^3+11*n^2-38*n+120)/24, n>1. - _R. J. Mathar_, Sep 12 2008
%F A141534 G.f.: x*(1-x+x^2+x^3-x^5)/(1-x)^5. - _Alexander R. Povolotsky_, Jun 06 2011
%Y A141534 Cf. A000217.
%K A141534 nonn,easy
%O A141534 1,2
%A A141534 Dan Graybill (clopen(AT)comcast.net), Aug 12 2008