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A350440
a(n) is the number of integers that can be represented in a 7-segment display by using only n segments (version A277116).
1
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.
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
Sequence in context: A249096 A249367 A257999 * A115449 A303851 A218542
KEYWORD
nonn,base,easy
AUTHOR
Stefano Spezia, Dec 31 2021
STATUS
approved