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 A146987 Triangle, read by rows, T(n, k) = binomial(n, k) for n < 2 and binomial(n, k) + 3^(n-1)*binomial(n-2, k -1) otherwise. 3
 1, 1, 1, 1, 5, 1, 1, 12, 12, 1, 1, 31, 60, 31, 1, 1, 86, 253, 253, 86, 1, 1, 249, 987, 1478, 987, 249, 1, 1, 736, 3666, 7325, 7325, 3666, 736, 1, 1, 2195, 13150, 32861, 43810, 32861, 13150, 2195, 1, 1, 6570, 45963, 137865, 229761, 229761, 137865, 45963, 6570, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1, 2, 7, 26, 124, 680, 3952, 23456, 140224, 840320, 5039872}. LINKS G. C. Greubel, Rows n = 0..100 of triangle, flattened FORMULA T(n, k) = binomial(n, k) for n < 2 and binomial(n, k) + 3^(n-1)*binomial(n-2, k -1) otherwise. EXAMPLE Triangle begins as:   1;   1,   1;   1,   5,   1;   1,  12,  12,    1;   1,  31,  60,   31,   1;   1,  86, 253,  253,  86,   1;   1, 249, 987, 1478, 987, 249, 1; MAPLE q:=3; seq(seq( `if`(n<2, binomial(n, k), binomial(n, k) + q^(n-1)*binomial(n-2, k-1)), k=0..n), n=0..10); # G. C. Greubel, Jan 09 2020 MATHEMATICA Table[If[n<2, Binomial[n, m], Binomial[n, m] + 3^(n-1)*Binomial[n-2, m-1]], {n, 0, 10}, {m, 0, n}]//Flatten PROG (PARI) T(n, k) = if(n<2, binomial(n, k), binomial(n, k) + 3^(n-1)*binomial(n-2, k-1) ); \\ G. C. Greubel, Jan 09 2020 (MAGMA) T:= func< n, k, q | n lt 2 select Binomial(n, k) else Binomial(n, k) + q^(n-1)*Binomial(n-2, k-1) >; [T(n, k, 3): k in [0..n], n in [0..10]]; // G. C. Greubel, Jan 09 2020 (Sage) @CachedFunction def T(n, k, q):     if (n<2): return binomial(n, k)     else: return binomial(n, k) + q^(n-1)*binomial(n-2, k-1) [[T(n, k, 3) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Jan 09 2020 (GAP) T:= function(n, k, q)     if n<2 then return Binomial(n, k);     else return Binomial(n, k) + q^(n-1)*Binomial(n-2, k-1); fi; end; Flat(List([0..10], n-> List([0..n], k-> T(n, k, 3) ))); # G. C. Greubel, Jan 09 2020 CROSSREFS Cf. A028262. Sequence in context: A174949 A174861 A110522 * A297915 A298508 A298328 Adjacent sequences:  A146984 A146985 A146986 * A146988 A146989 A146990 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Nov 04 2008 EXTENSIONS Edited by G. C. Greubel, Jan 09 2020 STATUS approved

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Last modified December 2 07:16 EST 2021. Contains 349437 sequences. (Running on oeis4.)