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 A235163 Number of positive integers with n digits in which adjacent digits differ by at most 1. 1
 9, 26, 75, 217, 629, 1826, 5307, 15438, 44941, 130900, 381444, 1111926, 3242224, 9455987, 27583372, 80472698, 234799873, 685149328, 1999414181, 5835044495, 17029601028, 49702671494, 145066398937, 423412132499, 1235854038791, 3607255734629, 10529101874491 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (6,-10,1,6,-1). FORMULA a(n) = Sum_{r=0..9} u(n,r) where u(n,r) = 0 if r<0 or r>9, u(1,0) = 0, u(1,r) = 1 for 1<=r<=9, and otherwise u(n,r) = u(n-1,r-1) + u(n-1,r) + u(n-1,r+1). G.f.: -x*(3*x^4-18*x^3-9*x^2+28*x-9)/(x^5-6*x^4-x^3+10*x^2-6*x+1). - Alois P. Heinz, Jan 12 2014 EXAMPLE a(2) = 26: 10, 11, 12, 21, 22, 23, 32, 33, 34, 43, 44, 45, 54, 55, 56, 65, 66, 67, 76, 77, 78, 87, 88, 89, 98, 99. MAPLE u:= proc(n, r) option remember; `if`(n=1, `if`(r=0, 0, 1),       add(`if`(r+i in [\$0..9], u(n-1, r+i), 0), i=-1..1))     end: a:= n-> add(u(n, r), r = 0..9): seq(a(n), n=1..30);  # Alois P. Heinz, Jan 12 2014 MATHEMATICA CoefficientList[Series[-x*(3*x^4-18*x^3-9*x^2+28*x-9)/(x^5-6*x^4-x^3+10*x^2-6*x+1), {x, 0, 30}], x]//Rest (* Harvey P. Dale, Aug 13 2019 *) PROG (Python) from functools import cache @cache def u(n, r):     if r < 0 or r > 9: return 0     if n == 1: return (r > 0)     return u(n-1, r-1) + u(n-1, r) + u(n-1, r+1) def a(n): return sum(u(n, r) for r in range(10)) print([a(n) for n in range(1, 28)]) # Michael S. Branicky, Sep 26 2021 CROSSREFS Cf. A032981, A090994, A126364 (allowing leading zeros). Sequence in context: A255108 A048771 A055849 * A084813 A322764 A325585 Adjacent sequences:  A235160 A235161 A235162 * A235164 A235165 A235166 KEYWORD nonn,base,easy AUTHOR Gerry Leversha, Jan 04 2014 STATUS approved

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Last modified July 1 18:20 EDT 2022. Contains 354974 sequences. (Running on oeis4.)