A350440 - OEIS

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

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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.