

A126635


a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digits 1,2,3, at least one of digits 4,5 and at least one of digits 6,7,8,9.


3



7, 47, 307, 1943, 11827, 69287, 392707, 2166743, 11703187, 62168327, 325983907, 1692105143, 8714154547, 44600020967, 227161443907, 1152585909143, 5830444893907, 29423488811207, 148206112628707, 745396075770743, 3744474953809267, 18792450661083047
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OFFSET

1,1


LINKS

Colin Barker, Table of n, a(n) for n = 1..1000
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Index entries for linear recurrences with constant coefficients, signature (15,85,225,274,120).


FORMULA

a(n) = 8*5^n16*4^n+14*3^n6*2^n+1.
G.f.: x*(120*x^4242*x^3+197*x^258*x+7) / ((x1)*(2*x1)*(3*x1)*(4*x1)*(5*x1)).  Colin Barker, Feb 22 2015


MAPLE

f:=n>8*5^n16*4^n+14*3^n6*2^n+1;


MATHEMATICA

LinearRecurrence[{15, 85, 225, 274, 120}, {7, 47, 307, 1943, 11827}, 30] (* Harvey P. Dale, Dec 31 2021 *)


PROG

(PARI) Vec(x*(120*x^4242*x^3+197*x^258*x+7) / ((x1)*(2*x1)*(3*x1)*(4*x1)*(5*x1)) + O(x^100)) \\ Colin Barker, Feb 22 2015


CROSSREFS

Cf. A125630, A125948, A125947, A125946, A125945, A125910, A125909, A125908, A125880, A125897, A125904, A125858.
Sequence in context: A198845 A323131 A229010 * A085352 A125370 A163346
Adjacent sequences: A126632 A126633 A126634 * A126636 A126637 A126638


KEYWORD

nonn,base,easy


AUTHOR

Aleksandar M. Janjic and Milan Janjic, Feb 08 2007


STATUS

approved



