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 A177351 Triangle t(n,k)= sum_{m=1..floor(n/2-k)} binomial(n-m-k,m+k), -floor(n/2) <= k <= floor(n/2), read by rows. 1
 0, 0, 2, 1, 0, 3, 2, 0, 5, 5, 4, 1, 0, 8, 8, 7, 3, 0, 13, 13, 13, 12, 7, 1, 0, 21, 21, 21, 20, 14, 4, 0, 34, 34, 34, 34, 33, 26, 11, 1, 0, 55, 55, 55, 55, 54, 46, 25, 5, 0, 89, 89, 89, 89, 89, 88, 79, 51, 16, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Row sums are 0, 0, 3, 5, 15, 26, 59, 101, 207, 350, 680,... The first column is essentially A000045, and the other columns also join the Fibonacci sequence after some transient initial terms. LINKS EXAMPLE 0; 0; 2, 1, 0; 3, 2, 0; 5, 5, 4, 1, 0; 8, 8, 7, 3, 0; 13, 13, 13, 12, 7, 1, 0; 21, 21, 21, 20, 14, 4, 0; 34, 34, 34, 34, 33, 26, 11, 1, 0; 55, 55, 55, 55, 54, 46, 25, 5, 0; 89, 89, 89, 89, 89, 88, 79, 51, 16, 1, 0; MATHEMATICA w[n_, m_, k_] = Binomial[n - (m + k), m + k]; t[n_, k_] := Sum[w[n, m, k], {m, 1, Floor[n/2 - k]}]; Table[Table[t[n, k], {k, -Floor[n/2], Floor[n/2]}], {n, 0, 10}]; Flatten[%] CROSSREFS Cf. A000045 Sequence in context: A225310 A131358 A291895 * A117901 A074984 A112658 Adjacent sequences:  A177348 A177349 A177350 * A177352 A177353 A177354 KEYWORD nonn,tabf AUTHOR Roger L. Bagula, Dec 10 2010 STATUS approved

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Last modified October 23 09:45 EDT 2019. Contains 328345 sequences. (Running on oeis4.)