A350440 a(n) is the number of integers that can be represented in a 7-segment display by using only n segments (version A277116).

0, 0, 1, 2, 3, 8, 12, 19, 33, 55, 103, 170, 297, 509, 875, 1531, 2622, 4546, 7828, 13514, 23379, 40313, 69680, 120232, 207630, 358597, 619066, 1069184, 1845894, 3187511, 5504024, 9503677, 16410894, 28336222, 48929611, 84487805, 145886994, 251908592, 434974763, 751085173

Offset: 0

Author

Stefano Spezia, Dec 31 2021

Keywords

• nonn
• base
• easy

Comments

The integers are displayed as in A277116, where the negative integers are depicted by using one more segment for the minus sign.

Since the integer 0 is depicted by 6 segments, in order to avoid considering -0 in the case n = 7, a(7) is obtained by decreasing of a unit the result of the sum A343315(7) + A343315(6) = 14 + 6 = 20, i.e., a(7) = 20 - 1 = 19.

Examples

			See illustration in Links section.
		

Links

• Stefano Spezia, Table of n, a(n) for n = 0..4000
• Stefano Spezia, Illustration for n = 7
• Index entries for linear recurrences with constant coefficients, signature (0,1,1,1,4,2,1).
• Index entries for sequences related to calculator display
• Index entries for sequences related to compositions

Crossrefs

Cf. A277116, A343315.

Programs

Mathematica

P[x_]:=x^2+x^3+x^4+4x^5+2x^6+x^7; c[n_]:=Coefficient[Sum[P[x]^k, {k, Max[1, Ceiling[n/7]], Floor[n/2]}], x, n]; b[n_]:=c[n]-c[n-6]; (* A343315 *)
a[n_]:=If[n!=7,b[n]+b[n-1],19]; Array[a, 40, 0]

Formula

a(7) = 19, otherwise a(n) = A343315(n) + A343315(n-1).

G.f.: x^2*(1 + 2*x + 2*x^2 + 5*x^3 + 6*x^4 + 2*x^5 - x^7 - x^8 - 4*x^9 - 2*x^10 - x^11)/(1 - x^2 - x^3 - x^4 - 4*x^5 - 2*x^6 - x^7).

a(n) = a(n-2) + a(n-3) + a(n-4) + 4*a(n-5) + 2*a(n-6) + a(n-7) for n > 13.