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.
%I A134311 #37 May 04 2022 01:13:40 %S A134311 1,2,7,20,51,122,281,632,1399,3062,6645,14324,30707,65522,139249, %T A134311 294896,622575,1310702,2752493,5767148,12058603,25165802,52428777, %U A134311 109051880,226492391,469762022,973078501,2013265892,4160749539 %N A134311 Row sums of triangle A134310. %H A134311 M. F. Hasler, <a href="/A134311/b134311.txt">Table of n, a(n) for n = 0..1000</a> (terms a(0..999) from Gennady Eremin), May 03 2022 %H A134311 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,12,-4). %F A134311 Binomial transform of [1, 1, 4, 4, 6, 6, 8, 8, 10, 10, 12, 12, ...]. %F A134311 For n > 0, a(n) = (n+3)*2^(n-1) - n - 1. - _R. J. Mathar_, Apr 04 2012, edited by _M. F. Hasler_, Mar 29 2022 %F A134311 G.f.: (2*x^4-8*x^3+8*x^2-4*x+1)/((x-1)^2*(2*x-1)^2). - _Colin Barker_, Aug 13 2012 %e A134311 a(3) = 20 = sum of row 4 terms of triangle A134310: (4 + 4 + 5 + 7). %e A134311 a(3) = 20 = (1, 3, 3, 1) dot (1, 1, 4, 4) = (1 + 3 + 12 + 4). %t A134311 Join[{1},LinearRecurrence[{6,-13,12,-4},{2,7,20,51},30]] (* _Harvey P. Dale_, Apr 16 2013 *) %o A134311 (Python) %o A134311 a = lambda n: (n+3)*2**(n-1)-n-1 if n > 0 else 1 %o A134311 print([a(n) for n in range(40)]) # _Gennady Eremin_, Mar 26 2022 %o A134311 (PARI) apply( {A134311(n)=max(n+3,4)<<(n-1)-n-1}, [0..33]) \\ _M. F. Hasler_, Mar 29 2022 %Y A134311 Cf. A134310. %K A134311 nonn,easy %O A134311 0,2 %A A134311 _Gary W. Adamson_, Oct 21 2007 %E A134311 Offset corrected to 0 by _M. F. Hasler_, Mar 29 2022