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 A144961 Eigentriangle whose left border is the Padovan sequence, and whose right border and row sums are a modified Fibonacci sequence. 1
 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 1, 0, 0, 3, 1, 1, 0, 1, 0, 0, 5, 1, 1, 1, 0, 2, 0, 0, 8, 2, 1, 1, 1, 0, 3, 0, 0, 13, 2, 2, 1, 1, 2, 0, 5, 0, 0, 21, 3, 2, 2, 1, 2, 3, 0, 8, 0, 0, 34, 4, 3, 2, 2, 2, 3, 5, 0, 13, 0, 0, 55, 5, 4, 3, 2, 4, 3, 5 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,15 COMMENTS Left border = A000931, the Padovan sequence: (1, 0, 0, 1, 0, 1, 1, 1, 2, 2, ...). Right border = (1, 1, 1, 1, 2, 3, 5, 8, 13, 21, ...) Row sums = (1, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...). Sum of n-th row terms = rightmost term in next row. LINKS Nathaniel Johnston, Rows n = 0..150, flattened FORMULA Triangle read by rows, termwise products of a Padovan "decrescendo" triangle: (1; 0,1; 0,0,1; 1,0,0,1,...) and the Fibonacci series preceded by two 1's: (1, 1, 1, 1, 2, 3, 5, 8, ...); (i.e., the INVERT transform of the Padovan sequence). a(n,k) = Fibonacci(max(k-1,1))*A000931(n-k). - Nathaniel Johnston, May 05 2011 EXAMPLE First few rows of the triangle: 1; 0, 1; 0, 0, 1; 1, 0, 0, 1; 0, 1, 0, 0, 2; 1, 0, 1, 0, 0, 3; 1, 1, 0, 1, 0, 0, 5; 1, 1, 1, 0, 2, 0, 0, 8; 2, 1, 1, 1, 0, 3, 0, 0, 13; 2, 2, 1, 1, 2, 0, 5, 0, 0, 21; 3, 2, 2, 1, 2, 3, 0, 8, 0, 0, 34; 4, 3, 2, 2, 2, 3, 5, 0, 13, 0, 0, 55; ... MAPLE with(combinat): A000931 := proc(n) option remember: if(n=0)then return 1: elif(n<=2)then return 0: else return procname(n-2)+procname(n-3): fi: end: A144961 := proc(n, k) return fibonacci(max(k-1, 1))*A000931(n-k) end:for n from 0 to 12 do for k from 0 to n do printf("%d, ", A144961(n, k)); od: printf("\n"); od: # Nathaniel Johnston, May 05 2011 CROSSREFS Cf. A000045, A000931. Sequence in context: A283000 A145765 A157424 * A144627 A135929 A346377 Adjacent sequences: A144958 A144959 A144960 * A144962 A144963 A144964 KEYWORD nonn,easy,tabl AUTHOR Gary W. Adamson, Sep 27 2008 EXTENSIONS Example triangle corrected by Nathaniel Johnston, May 05 2011 STATUS approved

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Last modified September 21 08:25 EDT 2023. Contains 365499 sequences. (Running on oeis4.)