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 A131923 Triangle read by rows: T(n,k) = binomial(n,k) + n. 2
 1, 2, 2, 3, 4, 3, 4, 6, 6, 4, 5, 8, 10, 8, 5, 6, 10, 15, 15, 10, 6, 7, 12, 21, 26, 21, 12, 7, 8, 14, 28, 42, 42, 28, 14, 8, 9, 16, 36, 64, 78, 64, 36, 16, 9, 10, 18, 45, 93, 135, 135, 93, 45, 18, 10, 11, 20, 55, 130, 220, 262, 220, 130, 55, 20, 11, 12, 22, 66 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums = A131924: (1, 4, 10, 20, 36, 62, 106, 184, ...). LINKS Muniru A Asiru, Table of n, a(n) for n = 0..5049 FORMULA A007318 + A002024 - A000012 = A007318 + A003056 as infinite lower triangular matrices. A002024 = (1; 2,2; 3,3,3;...); A007318 = Pascal's triangle and A000012 = (1; 1,1; 1,1,1;...). EXAMPLE First few rows of the triangle are: 1; 2, 2; 3, 4, 3; 4, 6, 6, 4; 5, 8, 10, 8, 5; 6, 10, 15, 15, 10, 6; 7, 12, 21, 26, 21, 12, 7; 8, 14, 28, 42, 42, 28, 14, 8; 9, 16, 36, 64, 78, 64, 36, 16, 9; 10, 18, 45, 93, 135, 135, 93, 45, 18, 10; ... MATHEMATICA T[n_, m_] = Binomial[n, m] + n; Table[Table[T[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%] (* Roger L. Bagula, Jul 30 2008 *) PROG (PARI) T(n, k) = binomial(n, k) + n \\ Charles R Greathouse IV, Oct 16 2013 (GAP) a:=Flat(List([0..10], n->List([0..n], k->Binomial(n, k)+n))); # Muniru A Asiru, Jul 16 2018 (Magma) /* As triangle */ [[Binomial(n, k) + n: k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Jul 17 2018 CROSSREFS Cf. A002024, A007318, A000012, A003056, A131924 (row sums), A003991. Sequence in context: A319840 A368310 A003991 * A119457 A241356 A065157 Adjacent sequences: A131920 A131921 A131922 * A131924 A131925 A131926 KEYWORD nonn,tabl,easy AUTHOR Gary W. Adamson, Jul 29 2007 EXTENSIONS Edited, changing formula by Roger L. Bagula, Jul 30 2008 New name from Franklin T. Adams-Watters, Oct 16 2013 Terms 54 onwards from Muniru A Asiru, Jul 16 2018 STATUS approved

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Last modified March 1 05:26 EST 2024. Contains 370430 sequences. (Running on oeis4.)