The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A322628 Number of n-digit decimal numbers containing a fixed 2-digit integer with distinct digits as a substring. 5
 0, 0, 1, 19, 279, 3671, 45431, 540639, 6260959, 71068951, 794428551, 8773216559, 95937737039, 1040604153831, 11210103801271, 120060433858879, 1279394234787519, 13573881914016311, 143459424905375591, 1511020367139739599, 15866744246492020399 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS First differences of A322052. - Jon E. Schoenfield, Jul 31 2021 See A138288 for the number of n-digit decimal numbers that do not contain a fixed 2-digit integer with distinct digits as a substring. LINKS Colin Barker, Table of n, a(n) for n = 0..500 Index entries for linear recurrences with constant coefficients, signature (20,-101,10). FORMULA a(n) = 10*a(n-1) - a(n-2) + 9*10^(n-3) with a(0) = a(1) = 0, a(2) = 1. G.f.: x^2*(x-1)/((10*x-1)*(x^2-10*x+1)). - Alois P. Heinz, Dec 20 2018 a(n) = (27*10^n + 5*(5-2*sqrt(6))^n*(-3+sqrt(6)) - 5*(3+sqrt(6))*(5+2*sqrt(6))^n) / 30 for n>0. - Colin Barker, Dec 21 2018 MAPLE seq(coeff(series(x^2*(x-1)/((10*x-1)*(x^2-10*x+1)), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Dec 21 2018 PROG (Python) def find_int(i): if i == 0: return (0) intlist = [0, 1, 19] for n in range(4, i+2): if n > 3: a = 10*(intlist[n-2])+(9*10**(n-3)-intlist[n-3]) intlist.append(a) return (intlist[i-1]) for i in range(100): print(find_int(i), end=', ') (PARI) concat([0, 0], Vec(x^2*(x-1)/((10*x-1)*(x^2-10*x+1)) + O(x^30))) \\ Colin Barker, Dec 21 2018 (GAP) a:=[0, 1, 19];; for n in [4..20] do a[n]:=20*a[n-1]-101*a[n-2]+10*a[n-3]; od; Concatenation([0], a); # Muniru A Asiru, Dec 21 2018 CROSSREFS Cf. A255372, A138288, A322052, A004189. Sequence in context: A016187 A016184 A197742 * A322053 A328916 A081045 Adjacent sequences: A322625 A322626 A322627 * A322629 A322630 A322631 KEYWORD nonn,base,easy,changed AUTHOR Owen M Sheff, Dec 20 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 20 22:57 EDT 2023. Contains 361392 sequences. (Running on oeis4.)