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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).

%I A350438 #14 Jan 11 2022 22:05:08
%S A350438 0,0,1,1,3,6,11,14,23,39,71,118,195,317,537,906,1533,2550,4261,7119,
%T A350438 11973,20073,33650,56277,94286,157960,264843,443656,743269,1244915,
%U A350438 2085970,3494922,5855965,9810370,16436113,27536138,46135634,77295509,129501787,216963199,363500178
%N A350438 a(n) is the number of integers that can be represented in a 7-segment display by using only n segments (version A010371).
%C A350438 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.
%C A350438 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.
%H A350438 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,2,3,3,1).
%H A350438 <a href="/index/Ca#calculatordisplay">Index entries for sequences related to calculator display</a>
%H A350438 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A350438 a(7) = 14, otherwise a(n) = A331530(n) + A331530(n-1).
%F A350438 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).
%F A350438 a(n) = a(n-2) + 2*a(n-4) + 3*a(n-5) + 3*a(n-6) + a(n-7) for n > 13.
%e A350438 a(7) = 14 since -111, -71, -41, -17, -14, -9, -6, 8, 12, 13, 15, 21, 31 and 51 are displayed by 7 segments.
%e A350438                       __                              __
%e A350438   __   |  |  |    __ |  |  |    __ |__|  |    __   | |  |    __   | |__|
%e A350438        |  |  |          |  |          |  |         |    |         |    |
%e A350438        (-111)        (-71)         (-41)          (-17)          (-14)
%e A350438       __         __      __        __        __        __     __
%e A350438   __ |__|    __ |__     |__|    |  __|    |  __|    | |__     __|  |
%e A350438       __|       |__|    |__|    | |__     |  __|    |  __|   |__   |
%e A350438     (-9)       (-6)     (8)      (12)      (13)      (15)      (21)
%e A350438   __         __
%e A350438   __|  |    |__   |
%e A350438   __|  |     __|  |
%e A350438    (31)       (51)
%t A350438 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 *)
%t A350438 a[n_]:=If[n!=7,b[n]+b[n-1],14]; Array[a, 41, 0]
%Y A350438 Cf. A010371, A331530.
%K A350438 nonn,base,easy
%O A350438 0,5
%A A350438 _Stefano Spezia_, Dec 31 2021