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A209599 Triangle T(n,k), read by rows, given by (2, -1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. 1
1, 2, 0, 3, 1, 0, 5, 3, 0, 0, 8, 7, 1, 0, 0, 13, 15, 4, 0, 0, 0, 21, 30, 12, 1, 0, 0, 0, 34, 58, 31, 5, 0, 0, 0, 0, 55, 109, 73, 18, 1, 0, 0, 0, 0, 89, 201, 162, 54, 6, 0, 0, 0, 0, 0, 144, 365, 344, 145, 25, 1, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A skew version of A122075.

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

FORMULA

G.f.: (1+x)/(1-x-(1+y)*x^2).

T(n,k) = T(n-1,k) + T(n-2,k) + T(n-2,k-1), T(0,0) = 1, T(1,0) = 2, T(1,1) = 0, T(n,k) = 0 if k<0 or if k>n.

Sum_{k, 0<=k<=n} T(n,k)*x^k = A040000(n), A000045(n+2), A000079(n), A006138(n), A026597(n), A133407(n), A133467(n), A133469(n), A133479(n), A133558(n), A133577(n), A063092(n) for x = -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 respectively.

EXAMPLE

Triangle begins :

  1

  2, 0

  3, 1, 0

  5, 3, 0, 0

  8, 7, 1, 0, 0

  13, 15, 4, 0, 0, 0

  21, 30, 12, 1, 0, 0, 0

  34, 58, 31, 5, 0, 0, 0, 0

  55, 109, 73, 18, 1, 0, 0, 0, 0

  89, 201, 162, 54, 6, 0, 0, 0, 0, 0

  144, 365, 344, 145, 25, 1, 0, 0, 0, 0, 0

  ...

MATHEMATICA

T[0, 0] := 1; T[1, 0] := 2; T[1, 1] := 0; T[n_, k_] := T[n, k] = If[n<0, 0, If[k > n, 0, T[n - 1, k] + T[n - 2, k] + T[n - 2, k - 1]]]; Table[T[n, k], {n, 0, 49}, {k, 0, n}] // Flatten (* G. C. Greubel, Dec 19 2017 *)

CROSSREFS

Cf. A122075, A122950, A000045, A023610, A129707

Sequence in context: A225084 A238345 A299070 * A238347 A170942 A325660

Adjacent sequences:  A209596 A209597 A209598 * A209600 A209601 A209602

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Mar 10 2012

STATUS

approved

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Last modified January 19 18:13 EST 2020. Contains 331051 sequences. (Running on oeis4.)