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A140406 a(n) = binomial(n+6, 6)*8^n. 7
1, 56, 1792, 43008, 860160, 15138816, 242221056, 3598712832, 50381979648, 671759728640, 8598524526592, 106309030510592, 1275708366127104, 14915974742409216, 170468282770391040, 1909244767028379648 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

With a different offset, number of n-permutations (n >= 6) of 9 objects: p, r, s, t, u, v, z, x, y with repetition allowed, containing exactly six (6) u's.

If n=6 then a(0)=1.

Example: a(1)=56 because we have

uuuuuup, uuuuupu, uuuupuu, uuupuuu, uupuuuu, upuuuuu, puuuuuu,

uuuuuur, uuuuuru, uuuuruu, uuuruuu, uuruuuu, uruuuuu, ruuuuuu,

uuuuuus, uuuuusu, uuuusuu, uuusuuu, uusuuuu, usuuuuu, suuuuuu,

uuuuuut, uuuuutu, uuuutuu, uuutuuu, uutuuuu, utuuuuu, tuuuuuu,

uuuuuuv, uuuuuvu, uuuuvuu, uuuvuuu, uuvuuuu, uvuuuuu, vuuuuuu,

uuuuuuz, uuuuuzu, uuuuzuu, uuuzuuu, uuzuuuu, uzuuuuu, zuuuuuu,

uuuuuux, uuuuuxu, uuuuxuu, uuuxuuu, uuxuuuu, uxuuuuu, xuuuuuu,

uuuuuuy, uuuuuyu, uuuuyuu, uuuyuuu, uuyuuuu, uyuuuuu, yuuuuuu.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Index entries for linear recurrences with constant coefficients, signature (56, -1344, 17920, -143360, 688128, -1835008, 2097152).

FORMULA

G.f.: 1/(1-8*x)^7. - Zerinvary Lajos, Aug 06 2008

a(n) = 56*a(n-1) - 1344*a(n-2) + 17920*a(n-3) - 143360*a(n-4) + 688128*a(n-5) - 1835008*a(n-6) + 2097152*a(n-7); a(0)=1, a(1)=56, a(2)=1792, a(3)=43008, a(4)=860160, a(5)=15138816, a(6)=242221056. - Harvey P. Dale, Dec 15 2011

MAPLE

seq(binomial(n+6, 6)*8^n, n=0..17);

MATHEMATICA

Table[Binomial[n+6, 6]8^n, {n, 0, 20}] (* or *) LinearRecurrence[ {56, -1344, 17920, -143360, 688128, -1835008, 2097152}, {1, 56, 1792, 43008, 860160, 15138816, 242221056}, 20] (* Harvey P. Dale, Dec 15 2011 *)

PROG

(MAGMA) [8^n* Binomial(n+6, 6): n in [0..20]]; // Vincenzo Librandi, Oct 16 2011

(PARI) a(n)=binomial(n+6, 6)<<(3*n) \\ Charles R Greathouse IV, Dec 15 2011

CROSSREFS

Cf. A000579, A002409, A036220, A036226, A050988, A054337, A140405.

Sequence in context: A258465 A050989 A333067 * A075512 A223958 A000504

Adjacent sequences:  A140403 A140404 A140405 * A140407 A140408 A140409

KEYWORD

nonn,easy

AUTHOR

Zerinvary Lajos, Jun 16 2008

STATUS

approved

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Last modified January 24 21:49 EST 2022. Contains 350565 sequences. (Running on oeis4.)