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A254662 Numbers of words on alphabet {0,1,...,7} with no subwords ii, where i is from {0,1,...,4}. 1
1, 8, 59, 437, 3236, 23963, 177449, 1314032, 9730571, 72056093, 533584364, 3951258827, 29259564881, 216670730648, 1604473809179, 11881328856197, 87982723420916, 651523050515003, 4824609523867769, 35726835818619392, 264561679301939051, 1959112262569431533 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (7,3).

FORMULA

G.f.: (1 + x)/(1 - 7*x -3*x^2).

a(n) = 7*a(n-1) + 3*a(n-2) with n>1, a(0) = 1, a(1) = 8.

a(n) = (2^(-1-n) * ((7-sqrt(61))^n * (-9+sqrt(61)) + (7+sqrt(61))^n * (9+sqrt(61)))) / sqrt(61). - Colin Barker, Sep 08 2016

MATHEMATICA

RecurrenceTable[{a[0] == 1, a[1] == 8, a[n] == 7 a[n - 1] + 3 a[n - 2]}, a[n], {n, 0, 20}]

PROG

(MAGMA) [n le 1 select 8^n else 7*Self(n)+3*Self(n-1): n in [0..20]];

(PARI) Vec((1+x)/(1-7*x-3*x^2) + O(x^30)) \\ Colin Barker, Sep 08 2016

CROSSREFS

Cf. A015559, A055099, A126473, A126501, A126528, A254598, A254602.

Sequence in context: A343089 A112424 A190977 * A186362 A285231 A264817

Adjacent sequences:  A254659 A254660 A254661 * A254663 A254664 A254665

KEYWORD

nonn,easy

AUTHOR

Milan Janjic, Feb 04 2015

STATUS

approved

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Last modified May 18 16:07 EDT 2021. Contains 343995 sequences. (Running on oeis4.)