A152777 7 times heptagonal numbers: a(n) = 7*n*(5*n-3)/2.
0, 7, 49, 126, 238, 385, 567, 784, 1036, 1323, 1645, 2002, 2394, 2821, 3283, 3780, 4312, 4879, 5481, 6118, 6790, 7497, 8239, 9016, 9828, 10675, 11557, 12474, 13426, 14413, 15435, 16492, 17584, 18711, 19873, 21070, 22302, 23569, 24871, 26208, 27580, 28987, 30429
Offset: 0
Links
- Ivan Panchenko, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Crossrefs
Cf. A000566.
Programs
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Magma
[ 7*n*(5*n-3)/2 : n in [0..50] ]; // Wesley Ivan Hurt, Jun 09 2014
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Maple
A152777:=n->(35*n^2 - 21*n)/2; seq(A152777(n), n=0..100); # Wesley Ivan Hurt, Mar 04 2014
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Mathematica
s=0;lst={s};Do[s+=n;AppendTo[lst,s],{n,7,8!,35}];lst (* Vladimir Joseph Stephan Orlovsky, Apr 03 2009 *) 7*PolygonalNumber[7,Range[0,40]] (* Harvey P. Dale, Jun 03 2024 *) -
PARI
a(n)=7*n*(5*n-3)/2 \\ Charles R Greathouse IV, Jun 17 2017
Formula
a(n) = (35*n^2 - 21*n)/2 = 7*A000566(n).
a(n) = a(n-1) + 35*n - 28 (with a(0)=0). - Vincenzo Librandi, Dec 15 2010
From Elmo R. Oliveira, Dec 24 2024: (Start)
G.f.: 7*x*(1 + 4*x)/(1 - x)^3.
E.g.f.: 7*exp(x)*x*(2 + 5*x)/2.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 3. (End)
Comments