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A350439 a(n) is the number of integers that can be represented in a 7-segment display by using only n segments (version A063720).

%I A350439 #16 Jan 11 2022 22:05:18
%S A350439 0,0,1,2,3,9,12,20,35,58,116,180,329,560,970,1742,2933,5213,8954,
%T A350439 15627,27340,47171,82661,143054,249474,434167,754011,1314511,2282754,
%U A350439 3975774,6914639,12026735,20933900,36399440,63351409,110191798,191708837,333553521,580209879
%N A350439 a(n) is the number of integers that can be represented in a 7-segment display by using only n segments (version A063720).
%C A350439 The integers are displayed as in A063720, where the negative integers are depicted by using 1 segment more for the minus sign.
%C A350439 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 A343314(7) + A343314(6) = 16 + 5 = 21, i.e., a(7) = 21 - 1 = 20.
%H A350439 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,1,5,1,1).
%H A350439 <a href="/index/Ca#calculatordisplay">Index entries for sequences related to calculator display</a>
%H A350439 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A350439 a(7) = 20, otherwise a(n) = A343314(n) + A343314(n-1).
%F A350439 G.f.: x^2*(1 + 2*x + 2*x^2 + 6*x^3 + 6*x^4 + x^5 - x^7 - x^8 - 5*x^9 - x^10 - x^11)/(1 - x^2 - x^3 - x^4 - 5*x^5 - x^6 - x^7).
%F A350439 a(n) = a(n-2) + a(n-3) + a(n-4) + 5*a(n-5) + a(n-6) + a(n-7) for n > 13.
%e A350439 a(7) = 20 since -111, -77, -41, -14, 8, 12, 13, 15, 16, 19, 21, 31, 47, 51, 61, 74, 91, 117, 171 and 711 are displayed by 7 segments.
%e A350439                       __  __                                    __
%e A350439   __   |  |  |    __    |   |    __  |__|  |    __   | |__|    |__|
%e A350439        |  |  |          |   |           |  |         |    |    |__|
%e A350439       (-111)          (-77)          (-41)          (-14)       (8)
%e A350439       __        __         __                    __      __
%e A350439   |   __|    |  __|    |  |__     |  |__     |  |__|     __|  |
%e A350439   |  |__     |  __|    |   __|    |  |__|    |     |    |__   |
%e A350439    (12)       (13)      (15)       (16)       (19)        (21)
%e A350439   __               __      __                      __
%e A350439   __|   |    |__|    |    |__    |    |__    |       |  |__|
%e A350439   __|   |       |    |     __|   |    |__|   |       |     |
%e A350439    (31)         (47)        (51)        (61)          (74)
%e A350439    __                 __         __          __
%e A350439   |__|   |      |   |   |      |   |   |       |   |   |
%e A350439      |   |      |   |   |      |   |   |       |   |   |
%e A350439     (91)          (117)          (171)           (711)
%t A350439 P[x_]:=x^2+x^3+x^4+5x^5+x^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]; (* A343314 *)
%t A350439 a[n_]:=If[n!=7,b[n]+b[n-1],20];Array[a, 39, 0]
%Y A350439 Cf. A063720, A343314.
%K A350439 nonn,base,easy
%O A350439 0,4
%A A350439 _Stefano Spezia_, Dec 31 2021