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 A147289 A multi-shifted and scaled Pascal triangle: t(n,m)=Binomial[n, m] + Sum[If[n >= 2*k,2*Binomial[n - 2*k, m - k], 0], {k, 1, Floor[n/2]}]. 0
 1, 1, 1, 1, 4, 1, 1, 5, 5, 1, 1, 6, 12, 6, 1, 1, 7, 18, 18, 7, 1, 1, 8, 25, 38, 25, 8, 1, 1, 9, 33, 63, 63, 33, 9, 1, 1, 10, 42, 96, 128, 96, 42, 10, 1, 1, 11, 52, 138, 224, 224, 138, 52, 11, 1, 1, 12, 63, 190, 362, 450, 362, 190, 63, 12, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The row sums are: {1, 2, 6, 12, 26, 52, 106, 212, 426, 852, 1706, ...}. LINKS FORMULA t(n,m)=Binomial[n, m] + Sum[If[n >= 2*k,2*Binomial[n - 2*k, m - k], 0], {k, 1, Floor[n/2]}]. EXAMPLE {1}, {1, 1}, {1, 4, 1}, {1, 5, 5, 1}, {1, 6, 12, 6, 1}, {1, 7, 18, 18, 7, 1}, {1, 8, 25, 38, 25, 8, 1}, {1, 9, 33, 63, 63, 33, 9, 1}, {1, 10, 42, 96, 128, 96, 42, 10, 1}, {1, 11, 52, 138, 224, 224, 138, 52, 11, 1}, {1, 12, 63, 190, 362, 450, 362, 190, 63, 12, 1} MATHEMATICA Table[Binomial[n, m] + Sum[If[n >= 2*k, 2*Binomial[n - 2*k, m - k], 0], {k, 1, Floor[n/2]}], {n, 0, 10}, {m, 0, n}]; Flatten[%] CROSSREFS Sequence in context: A173740 A028275 A173118 * A147566 A204621 A146770 Adjacent sequences:  A147286 A147287 A147288 * A147290 A147291 A147292 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Nov 04 2008 EXTENSIONS Edited by N. J. A. Sloane, Nov 07 2008 STATUS approved

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Last modified October 16 09:29 EDT 2019. Contains 328056 sequences. (Running on oeis4.)