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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, 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
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.
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.
__ __
__ | | | __ | | | __ |__| | __ | | | __ | |__|
| | | | | | | | | | |
(-111) (-71) (-41) (-17) (-14)
__ __ __ __ __ __ __
__ |__| __ |__ |__| | __| | __| | |__ __| |
__| |__| |__| | |__ | __| | __| |__ |
(-9) (-6) (8) (12) (13) (15) (21)
__ __
__| | |__ |
__| | __| |
(31) (51)
MATHEMATICA
P[x_]:=x^2+2x^4+3x^5+3x^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]; (* A331530 *)
a[n_]:=If[n!=7, b[n]+b[n-1], 14]; Array[a, 41, 0]
CROSSREFS
Sequence in context: A342954 A015823 A049620 * A329741 A310096 A310097
KEYWORD
nonn,base,easy
AUTHOR
Stefano Spezia, Dec 31 2021
STATUS
approved