A143103 Row sums of triangle A143102.

1, 5, 17, 29, 54, 96, 138, 202, 292, 382, 503, 659, 815, 1011, 1251, 1491, 1780, 2122, 2464, 2864, 3326, 3788, 4317, 4917, 5517, 6193, 6949, 7705, 8546, 9476, 10406, 11430, 12552, 13674, 14899, 16231, 17563, 19007, 20567, 22127, 23808, 25614, 27420, 29356, 31426

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-4,2,-1,2,-1).

Formula

a(n) = Sum_{k=1..n} k*A143097(k).

G.f.: x*(1 + 3*x + 8*x^2 - 2*x^3 + 7*x^4 + x^5 + x^6 - x^7)/((1 - x)^4*(1 + x + x^2)^2). - Andrew Howroyd, Sep 21 2025

Example

a(4) = 29 = sum of row 4 terms of triangle A143102: (3 + 7 + 9 + 10).
a(4) = 29 since A143097 = (1, 2, 4, 3, 5,...) with n*A143097(n) = (1, 4, 12, 12, 25, 42,...) and 29 = (1 + 4 + 12 + 12).

Prog

(PARI) Vec((1 + 3*x + 8*x^2 - 2*x^3 + 7*x^4 + x^5 + x^6 - x^7)/((1 - x)^4*(1 + x + x^2)^2) + O(x^50)) \\ Andrew Howroyd, Sep 21 2025

Crossrefs

Cf. A143097, A143102.

Sequence in context: A220082 A207337 A145478 * A091851 A079292 A246334

Adjacent sequences: A143100 A143101 A143102 * A143104 A143105 A143106

Keyword

nonn,easy

Author

Gary W. Adamson, Jul 24 2008

Extensions

a(15) onwards from Andrew Howroyd, Sep 21 2025

Status

approved