A350438 - OEIS

A350438

a(n) is the number of integers that can be represented in a 7-segment display by using only n segments (version A010371).

0, 0, 1, 1, 3, 6, 11, 14, 23, 39, 71, 118, 195, 317, 537, 906, 1533, 2550, 4261, 7119, 11973, 20073, 33650, 56277, 94286, 157960, 264843, 443656, 743269, 1244915, 2085970, 3494922, 5855965, 9810370, 16436113, 27536138, 46135634, 77295509, 129501787, 216963199, 363500178

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OFFSET

0,5

COMMENTS

The integers are displayed as in A010371, where a 7 is depicted by 4 segments. The negative integers are depicted by using 1 segment more 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 A331530(7) + A331530(6) = 7 + 8 = 15, i.e., a(7) = 15 - 1 = 14.

LINKS

Table of n, a(n) for n=0..40.

Index entries for linear recurrences with constant coefficients, signature (0,1,0,2,3,3,1).

Index entries for sequences related to calculator display

Index entries for sequences related to compositions

FORMULA

a(7) = 14, otherwise a(n) = A331530(n) + A331530(n-1).

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

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

EXAMPLE

a(7) = 14 since -111, -71, -41, -17, -14, -9, -6, 8, 12, 13, 15, 21, 31 and 51 are displayed by 7 segments.

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