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A131913
Product of the square matrix in A065941 and the column vector (1, 2, 3, ...)'.
2
1, 3, 6, 13, 25, 48, 89, 163, 294, 525, 929, 1632, 2849, 4947, 8550, 14717, 25241, 43152, 73561, 125075, 212166, 359133, 606721, 1023168, 1722625, 2895843, 4861254, 8149933, 13646809, 22825200, 38136089, 63653827, 106146534, 176849517, 294401825, 489706272
OFFSET
0,2
FORMULA
a(n) = A010049(n) + A001629(n+2) = A055244(n+1) + A001629(n-1).
From Philippe Deléham, Dec 28 2013: (Start)
G.f.: (1+x-x^2)/(1-x-x^2)^2.
a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4), a(0)=1, a(1)=3, a(2)=6, a(3)=13.
a(n) = a(n-1) + a(n-2) + 2*Fibonacci(n). (End)
EXAMPLE
a(4) = 25 = (1, 1, 3, 2, 1) dot (1, 2, 3, 4, 5) = (1 + 2 + 9 + 8 + 5), where (1, 1, 3, 2, 1) = row 4 of triangle A065941.
a(4) = 25 = A010049(4) + A001629(6) = 5 + 20.
a(5) = 48 = A055244(6) + A001629(4) = 43 + 5.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Jul 27 2007
STATUS
approved