A254362 a(n) = 3*2^n + 3^n + 6.

10, 15, 27, 57, 135, 345, 927, 2577, 7335, 21225, 62127, 183297, 543735, 1618905, 4832127, 14447217, 43243335, 129533385, 388206927, 1163834337, 3489930135, 10466644665, 31393642527, 94168344657, 282479868135, 847389272745, 2542067154927, 7626000138177

Offset

0,1

Comments

This is the sequence of third terms of "third partial sums of m-th powers".

Is this 10 followed by A087719? [Bruno Berselli, Jan 30 2015]

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Luciano Ancora, Demonstration of formulas, page 1.

Luciano Ancora, Recurrence relations for partial sums of m-th powers

Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Formula

G.f.: -(47*x^2-45*x+10) / ((x-1)*(2*x-1)*(3*x-1)). - Colin Barker, Jan 30 2015

a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3). - Colin Barker, Jan 30 2015

Mathematica

Table[3 * 2^n + 3^n + 6, {n, 0, 29}] (* Alonso del Arte, Jan 29 2015 *)
LinearRecurrence[{6, -11, 6}, {10, 15, 27}, 30] (* Harvey P. Dale, Oct 11 2024 *)

Prog

(PARI) vector(30, n, n--; 3*2^n + 3^n + 6) \\ Colin Barker, Jan 30 2015

Crossrefs

Cf. A062709, A254363, A254364.

Sequence in context: A053330 A051990 A246447 * A373488 A182427 A171956

Adjacent sequences: A254359 A254360 A254361 * A254363 A254364 A254365

Keyword

nonn,easy

Author

Luciano Ancora, Jan 29 2015

Status

approved