cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A074149 Sum of terms in each group in A074147.

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%I A074149 #28 Aug 30 2022 14:01:16
%S A074149 1,6,15,36,65,114,175,264,369,510,671,876,1105,1386,1695,2064,2465,
%T A074149 2934,3439,4020,4641,5346,6095,6936,7825,8814,9855,11004,12209,13530,
%U A074149 14911,16416,17985,19686,21455,23364,25345,27474,29679,32040,34481,37086
%N A074149 Sum of terms in each group in A074147.
%C A074149 The odd-indexed entries are the sums pertaining to the corresponding magic squares.
%H A074149 Harvey P. Dale, <a href="/A074149/b074149.txt">Table of n, a(n) for n = 1..1000</a>
%H A074149 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F A074149 a(2n-1) = 4n^3 - 6n^2 + 4n - 1, a(2n) = 4n^3 + 2n. a(n) = (n^3 + n)/2 if n odd, n^3/2 + n if n even. a(n) = n^3/2 + n(3 + (-1)^n)/4. - _Franklin T. Adams-Watters_, Jul 17 2006
%F A074149 G.f.: x*(x^2+1)*(x^2+4*x+1) / ( (1+x)^2*(x-1)^4 ). - _R. J. Mathar_, Mar 07 2011
%F A074149 E.g.f.: x*((2 + 3*x + x^2)*cosh(x) + (3 + 3*x + x^2)*sinh(x))/2. - _Stefano Spezia_, May 07 2021
%F A074149 a(n) = n*(n^2-A000035(n))/2 + n. - _Chai Wah Wu_, Aug 30 2022
%t A074149 LinearRecurrence[{2,1,-4,1,2,-1},{1,6,15,36,65,114},50] (* _Harvey P. Dale_, Jun 22 2016 *)
%o A074149 (PARI) a(n)=n^3/2 + n*(3+(-1)^n)/4 \\ _Charles R Greathouse IV_, Jun 11 2015
%o A074149 (Python)
%o A074149 def A074149(n): return (n*(n**2-(n&1))>>1)+n # _Chai Wah Wu_, Aug 30 2022
%Y A074149 Cf. A000035, A074147, A074148, A061925, A006003, A061804.
%K A074149 nonn,easy
%O A074149 1,2
%A A074149 _Amarnath Murthy_, Aug 28 2002
%E A074149 More terms from _Franklin T. Adams-Watters_, Jul 17 2006