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

0,4

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.

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

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.

Example

See illustration in Links section.

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]

Crossrefs

Cf. A277116, A343315.

Sequence in context: A249096 A249367 A257999 * A115449 A303851 A218542

Adjacent sequences: A350437 A350438 A350439 * A350441 A350442 A350443

Keyword

nonn,base,easy

Author

Stefano Spezia, Dec 31 2021

Status

approved