A350177 a(n) is the number of nonnegative integers that can be represented by lighting only n segments on a 9-segment display, used by the Russian postal service.
0, 0, 0, 2, 3, 2, 5, 13, 17, 22, 47, 86, 127, 211, 387, 645, 1044, 1794, 3086, 5135, 8608, 14674, 24805, 41631, 70322, 119069, 200768, 338429, 571845, 965823, 1629253, 2749904, 4643876, 7838862, 13229487, 22333638, 37704236, 63642469, 107427241, 181351098, 306133271
Offset: 0
Examples
a(6) = 5 since 0, 11, 17, 71 and 77 are displayed by 6 segments. _ _ _ _ _ | | /| /| /| / / /| / / |_| | | | | | | | | (0) (11) (17) (71) (77)
Links
- Steffen Eger, Restricted Weighted Integer Compositions and Extended Binomial Coefficients, Journal of Integer Sequences, Vol. 16, Article 13.1.3, (2013).
- Wikipedia, Postal code template.
- Wikipedia, Postal codes in Russia.
- Index entries for linear recurrences with constant coefficients, signature (0,0,2,3,2,1,1).
- Index entries for sequences related to calculator display
- Index entries for sequences related to compositions
Programs
-
Mathematica
P[x_]:=2x^3+3x^4+2x^5+x^6+x^7; b[n_]:=Coefficient[Sum[P[x]^k, {k, Max[1, Ceiling[n/7]], Floor[n/2]}], x, n]; a[n_]:=b[n]-b[n-6]; Array[a, 41, 0]
Formula
a(n) = b(n) - b(n-6), where b(n) = [x^n] Sum_{k=max(1,ceiling(n/7))..floor(n/2)} P(x)^k with P(x) = 2*x^3 + 3*x^4 + 2*x^5 + x^6 + x^7.
G.f.: x^3*(1 - x)*(1 + x)*(1 - x + x^2)*(1 + x + x^2)*(2 + 3*x + 2*x^2 + x^3 + x^4)/(1 - 2*x^3 - 3*x^4 - 2*x^5 - x^6 - x^7).
a(n) = 2*a(n-3) + 3*a(n-4) + 2*a(n-5) + a(n-6) + a(n-7) for n > 13.
Comments