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A120297 Sum of all matrix elements of n X n matrix M(i,j) = Fibonacci(i+j-1). 4
1, 5, 20, 65, 193, 544, 1489, 4005, 10660, 28193, 74273, 195200, 512257, 1343077, 3519412, 9219105, 24144289, 63224096, 165544721, 433437125, 1134810436, 2971065025, 7778499265, 20364618240, 53315655553, 139582833989 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

p^2 divides a(p-1) for p = 5, 11, 19, 29, 31, 41, 59, 61, 71, ... = A038872 (Primes congruent to {0, 1, 4} mod 5), also odd primes p such that where 5 is a square mod p. All squared prime divisors of a(n) also belong to A038872.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

FORMULA

a(n) = Sum_{j=1..n} Sum_{i=1..n} Fibonacci(i+j-1).

a(n) = Fibonacci(2*n+3) - 2*Fibonacci(n+3) + 2. - Vladeta Jovovic, Jul 21 2006

G.f.: (1 - x^3 + 2*x^2)/((x-1)*(x^2 + x - 1)*(x^2 - 3*x + 1)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 14 2009

EXAMPLE

Matrix begins:

  1  1  2  3  5

  1  2  3  5  8

  2  3  5  8 13

  3  5  8 13 21

  5  8 13 21 34

MATHEMATICA

Table[Sum[Sum[Fibonacci[i+j-1], {i, 1, n}], {j, 1, n}], {n, 1, 50}]

CROSSREFS

Cf. A000045, A038872, A001924, A062381.

Sequence in context: A160528 A023004 A001873 * A271066 A271599 A032286

Adjacent sequences:  A120294 A120295 A120296 * A120298 A120299 A120300

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Jul 11 2006

STATUS

approved

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Last modified November 19 14:52 EST 2018. Contains 317352 sequences. (Running on oeis4.)