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%I #43 Sep 08 2022 08:44:35
%S 0,1,14,54,136,275,486,784,1184,1701,2350,3146,4104,5239,6566,8100,
%T 9856,11849,14094,16606,19400,22491,25894,29624,33696,38125,42926,
%U 48114,53704,59711,66150,73036,80384,88209,96526,105350,114696,124579,135014,146016
%N a(n) = n^2*(5*n-3)/2.
%C Structured heptagonal prism numbers. - James A. Record (james.record(AT)gmail.com), Nov 07 2004
%C Apart from 0, partial sums of A220083. [_Bruno Berselli_, Dec 11 2012]
%D W. A. Whitworth, DCC Exercises in Choice and Chance, Stechert, NY, 1945, p. 29.
%H Vincenzo Librandi, <a href="/A006597/b006597.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = (1/6)*(15*n^3-9*n^2). - James A. Record (james.record(AT)gmail.com), Nov 07 2004
%F G.f.: x*(1+10*x+4*x^2)/(1-x)^4. - _Colin Barker_, Jun 08 2012
%F a(n) = Sum_{i=0..n-1} n*(5*i+1) for n>0. [_Bruno Berselli_, Sep 08 2015]
%F Sum_{n>=1} 1/a(n) = 1.1080093773051638036... = (sqrt(5*(5 - 2*sqrt(5)))*Pi - Pi^2 - 5*sqrt(5)*arccoth(sqrt(5)) + (25*log(5))/2)/9. - _Vaclav Kotesovec_, Oct 04 2016
%p A006597:=n->n^2*(5*n-3)/2; seq(A006597(n), n=0..40); # _Wesley Ivan Hurt_, Mar 11 2014
%t Table[n^2*(5*n-3)/2, {n, 0, 40}] (* _Wesley Ivan Hurt_, Mar 11 2014 *)
%o (Magma) [n^2*(5*n-3)/2: n in [0..40]]; // _Vincenzo Librandi_, Jul 20 2011
%o (PARI) a(n)=n^2*(5*n-3)/2; \\ _Joerg Arndt_, Jul 20 2011
%Y Cf. A100177 - structured prisms; A100145 for more on structured numbers.
%Y Cf. similar sequences, with the formula (k*n-k+2)*n^2/2, listed in A262000.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
%E Name corrected by _Arkadiusz Wesolowski_, Jul 20 2011
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