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A210982
Zero together with A126264 and positive terms of A051624 interleaved.
7
0, 1, 8, 12, 26, 33, 54, 64, 92, 105, 140, 156, 198, 217, 266, 288, 344, 369, 432, 460, 530, 561, 638, 672, 756, 793, 884, 924, 1022, 1065, 1170, 1216, 1328, 1377, 1496, 1548, 1674, 1729, 1862, 1920, 2060, 2121, 2268, 2332, 2486, 2553, 2714, 2784, 2952, 3025, 3200, 3276, 3458, 3537, 3726
OFFSET
0,3
COMMENTS
Vertex number of a square spiral similar to A195162.
This is the case k=5 of the formula b(n,k) = ( 2*(k+5)*n^2+2*(k+3)*n-(k+1)+(2*(k-1)*n+k+1)*(-1)^n )/16. Sequences of the same family: A093025 (k=-1, with an initial 0), A210977 (k=0), A006578 (k=1), A210978 (k=2), A181995 (k=3, with one 0 only), A210981 (k=4). - Luce ETIENNE, Oct 30 2014
FORMULA
G.f.: x*(1+7*x+2*x^2) / ( (1+x)^2*(1-x)^3 ). - R. J. Mathar, Aug 07 2012
a(n) = (10*n^2 +8*n -3 +(4*n+3)*(-1)^n)/8. - Luce ETIENNE, Oct 14 2014
E.g.f.: (1/8)*((10*x^3 + 18*x -3)*exp(x) - (4*x - 3)*exp(-x)). - G. C. Greubel, Aug 23 2017
Sum_{n>=1} 1/a(n) = 5/9 + (sqrt(1-2/sqrt(5))/6 + sqrt(1+2/sqrt(5))/8)*Pi + 7*log(phi)*sqrt(5)/24 - 5*log(5)/48, where phi is the golden ratio (A001622). - Amiram Eldar, Aug 21 2022
MATHEMATICA
Table[(10*n^2 + 8*n - 3 + (4*n + 3)*(-1)^n)/8, {n, 0, 50}] (* G. C. Greubel, Aug 23 2017 *)
PROG
(Magma) [(10*n^2+8*n-3+(4*n+3)*(-1)^n )/8: n in [0..60]]; // Vincenzo Librandi, Oct 31 2014
(PARI) my(x='x+O('x^50)); Vec(x*(1+7*x+2*x^2)/((1+x)^2*(1-x)^3)) \\ G. C. Greubel, Aug 23 2017
CROSSREFS
Members of this family are A093005, A210977, A006578, A210978, A181995, A210981, this sequence.
Sequence in context: A368129 A368130 A367894 * A067677 A045523 A006983
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Aug 03 2012
STATUS
approved