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A103245 Triangle read by rows: T(n,k) = binomial(2n+1, n-k)*Fibonacci(2k+1), 0 <= k <= n. 1
1, 3, 2, 10, 10, 5, 35, 42, 35, 13, 126, 168, 180, 117, 34, 462, 660, 825, 715, 374, 89, 1716, 2574, 3575, 3718, 2652, 1157, 233, 6435, 10010, 15015, 17745, 15470, 9345, 3495, 610, 24310, 38896, 61880, 80444, 80920, 60520, 31688, 10370, 1597, 92378 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

S. G. Guba, Problem No. 174, Issue No. 4, July-August 1965, p. 73 of Matematika v Skole.

LINKS

Table of n, a(n) for n=0..45.

V. E. Hoggatt, Jr. and L. Carlitz, Problem H-77, The Fibonacci Quarterly, 5, No. 3, 1967, 256-258.

FORMULA

T(n, k) = binomial(2n+1, n-k)*Fibonacci(2k+1), 0 <= k <= n.

EXAMPLE

Triangle begins:

    1;

    3,   2;

   10,  10,   5;

   35,  42,  35,  13;

  126, 168, 180, 117,  34;

MAPLE

with(combinat): T:=(n, k)->binomial(2*n+1, n-k)*fibonacci(2*k+1): for n from 0 to 9 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form

CROSSREFS

Column 0 is A001700. Column 1 is A024483. T(n, n)=A001519(n) (the odd-subscripted Fibonacci numbers). Row sums are the powers of 5 (A000351). Alternating row sums yield A054108.

Sequence in context: A302846 A214844 A214966 * A019242 A064367 A113980

Adjacent sequences:  A103242 A103243 A103244 * A103246 A103247 A103248

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch, Mar 19 2005

STATUS

approved

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Last modified April 18 06:44 EDT 2019. Contains 322209 sequences. (Running on oeis4.)